a particle is projected at an angle tita to the horizontal with an initial velocity U.if the maximum horizontal distance travelled is 20m and the greatest height reached is 10m.find U and Tita

  1. 👍 0
  2. 👎 0
  3. 👁 87
  1. the horizontal distance is

    x(t) = u cosθ t
    The time taken to go 20m is thus
    t = 20/(u cosθ)

    The trajectory is
    y(t) = u sinθ t - g/2 t^2
    We know that y=0 at 0 and 20/(u cosθ), so the max height is reached at 10/(u cosθ). So,

    u sinθ * 10/(u cosθ) - g/2 (100/(u^2 cos^2 θ) = 10

    y = tanθ x - g/(2 (u cosθ)^2) x^2

    We know that y(20) = 0 and y(10) = 10. So, approximating g as 5 m/s^2,

    20tanθ - 500/(u cosθ)^2 = 0
    10tanθ - 125/(u cosθ)^2 = 10

    u = 5/2 √10
    tanθ = (√5-1)/2

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. Initial vertical speed Vi = U sin theta
    constant horizontal speed = u = U cos theta

    horizontal problem
    20 = U cos theta * T where T is time in air

    vertical problem
    v = Vi - g t
    v = 0 at the top
    t at top = Vi/g
    g = 9.8 m/s^2 on earth
    t at top = Vi/9.8

    now at the top at 10 meters
    h = 0 + Vi t -4.9 t^2
    10 = Vi t - 4.9 t^2
    10 = Vi^2/9.8 - 4.9 Vi^2/96
    10 = Vi^2 (.051)
    Vi = 14 m/s
    t at top = 14/9.8 = 1.43 s
    total time in air = 2t = 4.29 s
    20 = u (4.29)
    so u = 4.67 m/s
    U = sqrt (4.67^2+14^2) = 14.8 m/s
    tan theta = 14/4.67
    theta = 71.6 degrees

    1. 👍 0
    2. 👎 0
    posted by Damon
  3. t at top = 14/9.8 = 1.43 s
    total time in air = 2t = 2.86 s
    20 = u (2.86)
    so u = 6.99 m/s
    U = sqrt (6.99^2+14^2) = 15.64 m/s
    tan theta = 14/6.99
    theta = 63.5 degrees

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A ball projected with an initial velocity u at an angle tita to the horizontal cover a horizontal range of 26m after 5sec. Cal. The value of u and tita? g=10ms-1

    asked by Jason on November 4, 2015
  2. physics

    An object is projected with velocity of 100m/s from the ground level at an angle tita at the vertical,if the total thme is 10s.calculate tita(g=10m/s)

    asked by Marnal on November 8, 2011
  3. Science (physics)

    A particle P is launched from a point O with an initial velocity of 60m/s at an angle of 30 degrees to the horizontal. At the same time, a second particle Q is projected in the opposite direction with initial speed of 50m/s from a

    asked by Joe on March 18, 2013
  4. physics

    Two projectiles A and B are projected at the same time in the same vertical plane. A is projected at a height of 2m above the ground making an angle of 30deg with the horizontal. B is projected with the velocity of 20m/s at an

    asked by ridhi on April 29, 2012
  5. science

    a particle is projected vertically upward with the velocity u m/s and after t(s) another particle is projected upwards from the same point and with the same initial velocity. proof that the particle will meet after a lapes of (u/g

    asked by Fatima on February 13, 2013
  6. physical

    a ball that was projected up at an angle of θ degrees with the horizontal has a flight time of 5.0s and covers a range of 49.0 m. find (a) the time it took to reach maximum height, (b) the horizontal and vertical components of

    asked by john on September 11, 2017
  7. science

    a particle ia projected upward with a velocity of u m/s and after an interval of t(s) anoda particle is projected upward from the same point and wit the same initial velocity.proof dat they will meet at a height of

    asked by Fatima on February 13, 2013
  8. physics

    A particle is projected vertically upwards with velocity of u.after t seconds particle is projected from some point with same velocity.How long does it take for the second particle to meet the first particle?

    asked by Anonymous on April 22, 2013
  9. AP physics

    A particle of mass 3.00 kg is projected vertically upward with an initial velocity of 20.0 m/s. Neglecting air resistance, the particle’s kinetic energy when it is 20 m above the initial position is:

    asked by ali on December 11, 2014
  10. Physics(science)

    A ball's projected at an angle X to the horizontal from a cliff 96 metres high and strikes the ground at a distance of 260 metres away from the cliff.The time of its flight is 7 seconds.If it's assumed that air resistance's

    asked by Jaden K Hove on April 17, 2013

More Similar Questions